Hey OP - I haven't read the whole thread, so apologies if what I'm about to say has been suggested. I really feel for you. This is exactly what happened when I bought my first flat.
The seller had the flat let out, so it was furnished for the tenant. I went in with an offer slightly under asking price and she said she'd include all furniture and white goods if I paid the asking price. As I was coming from rented accommodation with none of my own stuff, and it was only an extra £2k, I thought why not.
In the run up to exchange, the seller had written on the paperwork which lists the fixtures and fittings 'all items in flat, which is furnished, are included in the price'.
As I felt this was a bit vague ('items'), I requested to EA that I enter the property before exchange to take an inventory, which I shared with them pointing out the furniture that she could remove if she wanted and the stuff I definitely wanted to keep - chests of drawers, foot stools, mirrors etc.
After exchange, I visited the property and realised she had taken some of the items that were supposed to be included in the price. I immediately raised it with the EA and they reported back that the seller 'was not going to return the property nor pay any money to cover the cost of it'. The cheek!
This really p**sed me off, so I went onto the Which? website, where they have a template for a 'Letter before action' which is a legal letter that warns someone that you'll take them to the small claims court if they don't provide the goods or services promised.
I gave her 28 days to respond, and on day 27, she agreed to pay me money for the items she'd taken. Yaaasss!